Thermal management plays a critical role in the functionality and reliability of modern microelectronics. As the feature sizes of these devices continue to shrink, researchers have focused on understanding fundamental aspects of thermal transport at the nanoscale, and a variety of experimental techniques have been developed for this purpose (D. G. Cahill, et al., J. Appl. Phys. 93, 793 (2003); D. G. Cahill, et al., J. Heat Transfer 124, 223 (2002)). These include Scanning Thermal Microscopy (SThM), which is based on a heated atomic force microscope tip (O. Kwon, L. Shi, and A. Majumdar, ASME Trans. J. Heat Transfer 125, 156 (2003)), techniques using microfabricated thin film heaters such as the 3ω method (D. G. Cahill, Rev. Sci. Instrum. 61, 802 (1990)), and optical pump-probe methods such as Time-Domain Thermoreflectance (TDTR) (C. A. Paddock and G. L. Eesley, J. Appl. Phys. 60, 285 (1986); W. S. Capinski, et al., Phys. Rev. B 59, 8105 (1999); D. G. Cahill, Rev. Sci. Instrum. 75, 5119 (2004)) and Frequency-Domain Thermoreflectance (FDTR) (A. J. Schmidt, et al., Rev. Sci. Instrum. 80, 094901 (2009); J. Zhu, et al., J. Appl. Phys. 108, 094315 (2010); J. A. Malen, et al., J. Heat Transfer 133, 081601 (2011)). Each of these techniques has relative strengths and weaknesses for quantifying thermal properties in sub-micrometer thin films and across material interfaces. The 3∫ method is a reliable way to measure cross-plane thermal conductivity of materials, but it requires microfabrication, electrical contacts, and its spatial resolution is limited by the dimension of the strip heater deposited above the sample, while SThM provides imaging of thermal properties with nanometer-scale spatial resolution but is extremely sensitive to both sample and tip morphology and requires challenging probe fabrication and complex heat transfer modeling in order to obtain reliable results. TDTR and FDTR are noncontact optical pump-probe techniques, in which one beam of light (the pump) acts as a heat source while a second beam (the probe) detects the resulting temperature change through a change in surface reflectivity. Due to their accuracy and flexibility, they have become increasingly popular methods for determining the thermal properties of thin films.
In TDTR, there is a variable optical delay between the pump and probe pulses from an ultrafast pulsed laser source, while in FDTR the frequency of the modulated pump beam is varied. Both methods typically require the sample to be coated with a thin (˜100 nm) metal transducer layer with a high coefficient of thermoreflectance at the probe wavelength. Advantages of TDTR include picosecond temporal resolution, the capability to resolve non-equilibrium dynamics among energy carriers, and, for some samples, improved sensitivity to thermal interface conductance and the thermal properties of thin films (P. E. Hopkins, et al., J. Heat Transfer 132, 081302 (2010)). On the other hand, FDTR avoids the complexity of a mechanical delay stage and the high cost of a pulsed laser system, and with the right range of modulation frequencies, FDTR has similar or improved sensitivity for many types of thin-film thermal measurements (J. Zhu, et al., J. Appl. Phys. 108, 094315 (2010); J. A. Malen, et al., J. Heat Transfer 133, 081601 (2011); J. Liu, et al., Rev. Sci. Instrum. 84, 034902 (2013); A. J. Schmidt, et al., J. Appl. Phys. 107, 104907 (2010)).
Previously, TDTR has been used for thermal conductivity imaging of materials (S. Huxtable, et al., Nature Mater. 3, 298 (2004); E. Lopez-Honorato, et al., J. Nucl. Mater. 378, 35 (2008)). However, this method, which is essentially single-frequency thermal wave imaging, is not self-contained because an average volumetric heat capacity has to be assumed for the entire sample, and in addition requires a careful choice of optical delay to minimize the effect of the transducer layer on the measurement. Similarly, photothermal beam deflection techniques have been used to image thermal diffusivity (B. Li, et al., J. Eur. Ceram. Soc. 19, 1631 (1999)). However, again thermal conductivity and heat capacity cannot be separated, and the spatial resolution is limited by the need to offset the probe beam relative to the pump beam. Therefore, there remains an important role for a high-resolution imaging technique able to simultaneously map different thermal properties.